Is building the bedroom wing really necessary? Because, you do get beds anyways. So, im just looking for some advice on if I should build that wing or would that just be a waste of a wing?

It is not absolutely necessary. The main hall can have three beds - two small and one double. The double bed is for you (and your spouse, if you have one). If you don't adopt children, your housecarl and steward each get a small bed. If you do adopt, the kids take the small beds and your steward and housecarl don't sleep.

Personally, I don't like that last part from an RP perspective; I want my housecarl and steward to sleep. So I built the bedroom for the children, and me, my housecarl, and my steward have the main hall beds. But if non-sleeping NPCs in your house don't bother you - or if you don't intend to adopt children - then the bedroom is unecessary.

Another thing to consider: Are either of the other two options for that wing (greenhouse and enchanter's tower) something you really want? Because if you're absolutely dying to have one or the other, that's more reason not to build the bedroom. But if you don't care about having one of those, then the extra living space aforded by the bedroom is probably a good idea. Keep in mind that the other options are not any more necessary than the bedroom; you can have an enchanting table in your main hall, and you can grow some alchemy ingredients in the exterior garden that all houses have.

For my family home (Lakeview Manor) I went with bedroom, storage room, library. It has plenty of living space for my family and assorted hangers-on, I can enchant using the enchanter's table in the main hall, and even grow some ingredients in the garden. Plus I have the library for my ever-growing book collection and a balcony that wraps around the two sides of the house that really have a view. If I decide to build a second house I'll set it up differently, but that's pretty far off (if it happens at all). The setup I chose for my family home provides everything I really wanted.